Abstract
This paper presents a five-round algebraic property of the Advanced Encryption Standard (AES). In the proposed property, we modify twenty bytes from five intermediate values at some fixed locations in five consecutive rounds, and we show that after five rounds of operations, such modifications do not change the intermediate result and finally still produce the same ciphertext. We introduce an algorithm named δ, and the algorithm accepts a plaintext and a key as two inputs and outputs twenty bytes, which are used in the five-round property. We demonstrate that the δ algorithm has 20 variants for AES-128, 28 variants for AES-192 and 36 variants for AES-256. By employing the δ algorithm, we define a modified version of the AES algorithm, the δAES. The δAES calls the δ algorithm to generate twenty bytes, and uses these twenty bytes to modify the AES round keys. The δAES employs the same key scheduling algorithm, constants and round function as the AES. For a plaintext and a key, the AES and the δAES produce the same ciphertext.
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References
Daemen, J., Rijmen, V.: AES Proposal: Rijndael, AES Round 1 Technical Evaluation CD-1: Documentation, National Institute of Standards and Technology (1998)
Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer, Heidelberg (1993)
Matsui, M.: Linear Cryptoanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)
NIST: Federal Information Processing Standards (FIPS) 197: Advanced Encryption Standard (AES). National Institute of Standards and Technology (November 26, 2001)
Murphy, S., Robshaw, M.: Essential Algebraic Structure within the AES. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 1–16. Springer, Heidelberg (2002)
Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)
Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)
Barkan, E., Biham, E.: In How Many Ways Can You Write Rijndael? In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 160–175. Springer, Heidelberg (2002)
Gilbert, H., Minier, M.: A Collision Attack on 7 Rounds of Rijndael. In: The Third Advanced Encryption Standard Candidate Conference, pp. 230–241 (2000)
Daemen, J., Knudsen, L., Rijmen, V.: The Block Cipher Square. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997)
Ferguson, N., Kelsey, J., Lucks, S., Schneier, B., Stay, M., Wagner, D., Whiting, D.: Improved Cryptanalysis of Rijndael. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 213–230. Springer, Heidelberg (2001)
Lucks, S.: Attacking Seven Rounds of Rijndael under 192-bit and 256-bit Keys. In: The Third Advanced Encryption Standard Candidate Conference, pp. 215–229 (2000)
Akkar, M.L., Giraud, C.: An Implementation of DES and AES, Secure against Some Attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 309–318. Springer, Heidelberg (2001)
Golic, J., Tymen, C.: Multiplicative Masking and Power Analysis of AES. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 198–212. Springer, Heidelberg (2003)
Biryukov, A.: The Design of a Stream Cipher LEX. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 67–75. Springer, Heidelberg (2007)
Daemen, J., Rijmen, V.: A New MAC Construction ALRED and a Specific Instance ALPHA-MAC. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 1–17. Springer, Heidelberg (2005)
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Huang, J., Seberry, J., Susilo, W. (2008). A Five-Round Algebraic Property of the Advanced Encryption Standard. In: Wu, TC., Lei, CL., Rijmen, V., Lee, DT. (eds) Information Security. ISC 2008. Lecture Notes in Computer Science, vol 5222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85886-7_22
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DOI: https://doi.org/10.1007/978-3-540-85886-7_22
Publisher Name: Springer, Berlin, Heidelberg
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